Discussion
The total kinetic energy imparted to the water per second (in kW) by the pump is
Answer: C
The pump imparts 28 kW of kinetic energy.
In the boat's frame, water enters at 5 m/s and is discharged at 9 m/s, so the pump raises its kinetic energy per second by
\[ \begin{aligned} \dot{E} &= \tfrac{1}{2}\rho Q(V_{j}^{2} - V^{2}) \\ &= \tfrac{1}{2}(1000)(1)(81 - 25) = 28000\ \text{W} \end{aligned} \]
that is 28 kW. Of this, 20 kW goes into propelling the boat (the previous question) and the remaining 8 kW is left in the wake, which gives a propulsive efficiency of 20/28, about 71 percent. The option 81 uses only the jet speed, and 25 only the inlet speed.
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